Last updated October 23, 2009.
IMPORTANT INFORMATION:
Lunch lecture on November 3. Poster
Schedule of lecture topics, links to notes and resources and homework assignments.
Day and Date  Section 
Topics 
Notes 
Homework Problems Assigned 

M 
8/24 
1.1 
Rational and real numbers  Quiz. Definitions. Algorithms for converting rationals from decimal to fraction notation and vice versa. Notes  Convert 1/17 to decimal and convert 365.17365 to fraction. 
T 
8/25 
1.1 
Absolute value 
Notes  10: 15, 18, 21, 23, 24 
W 
8/26 
1.2 
Linear functions  Enumerating the rationals. Needs Mathematica; get student verion here.  19: 7, 8, 22, 24. Challenge Problem 
Th 
8/27 
 
Motion graphs, average rate of change.  Also showed nondenumerability of irrationals  Problem sheet 
F 
8/28 
2.1 
Instantaneous rate of change approximated by averages.  Reviewed equations of lines, and built on this.  58: 17, 66: 5 
M 
8/31 
2.1, 2.2 
Review, instananeous rate of change  Sample test  Sample test: "Ave. Rate of Ch." 3 
T 
9/1 
2.8 
Limits  Formal definition; problem p. 115: 33. Limits at infinity.  Read 2.8. Sample test: Limits,1,2. 
W 
9/2 
2.2 
More on limits  Examples of how a limit may fail to exist: break in graph, asymptote, oscillation.  77: 125 (odd) 
Th 
9/3 
2.4 
limits (cont.)  Continuity defined. Using "local equality" to compute limits. Factoring A^n B^n.  Prepare for test. Help session tonight in Prescott 212, 7PM. 
F 
9/4 
 
Test  Get a copy of the test: with answers  without answers. 
Hand in corrected test on Friday, 9/11. 
M 
9/7 
 
Labor Day Vacation     
T 
9/8 
2.3 
Review of test; limit rules.  Proofs of the limit rulesif you're interestedcan be found on page A18 (Appendix D).  82: 5, 10, 15, 20, 25, 30, 35, 40 
W 
9/8 
2.6 
Trig functions; Squeeze Thm.  Activity guide  HW 
Th 
9/10 
2.6 
Trig functions (cont.)  Do parts C. and D. of the Notes.  
F 
9/11 
2.7 
Intermediate Value Theorem (IVT)  
M 
9/14 
 
Proof of IVT  Notes on the theorems of calculus Thoughts about proof 
Ham Sandwich Theorem (page 1078) 
T 
9/15 
3.1 
Definition of derivative.  (Deduced the power rule.)  125: 29, 30, 32, 34, 37, 39 
W 
9/16 
3.2 
Derivatives as functions.  Leibniz notation. Linearity of differentiation.  139: 1, 3, 5, 7, 9 
Th 
9/17 
3.2 
Exponential function  
F 
9/18 
3.3 
Product and quotient rule  Deriving the quotient rule from the product rule and the reciprocal rule; examples.  148: 5, 10, 15, 20, 25, 30, 35 
M 
9/21 
3.3 
Deriving the reciprocal rule  More examples  148: 40, 45 
T 
9/22 
3.4 
Applications; estimation  Problem: if the surface area of a cube is 600 sq. ft. and it increase by 1 sq. ft., what is the increase in volume. Solved algebraically and by estimation with tangent line.  Estimate the cube root of 1001. 
W 
9/23 
3.5 
Higher derivatives  Formulae for d^n y/ dx^n; acceleration; pictures  165: 5, 9, 11, 25, 27, 33, 35, 39, 40 
Th 
9/24 
3.6, 3.7 
Trig. functions. Chain Rule.  Proof of chain rule. Leibniz notation versus functional notation. Examples.  170: 9, 11, 15, 32, 37. 178: 5, 11, 13, 21, 22. 
F 
9/25 
3.7 
Chain Rule  Activities with differential equations  
M 
9/28 
3.8 
Implicit differentiation  185: 11, 19, 31  
T 
9/29 
QUIZ. Inverse functions.  "Money is the eats of all roovels."  Suppose f and g are inverses and let y = f(x). 1a) Differentiate the equation f(g(x)) = x with respect to x. Then use the result to express g' in terms of f' and g. (See page 187). 1b) If y = f(x), then f'(a) = dy/dx evaluated when x = a. Similarly, g'(b) = 1/(dy/dx) evaluated when WHAT = b? 1c) Does it make sense to say that dx/dy is the derivative of g? 2) If g is the inverse of the exponential function, what is g'? (For help, see p. 193.)  
W 
9/30 
3.9 
Derivatives of inverse trig functions  191: 11, 13 19, 23. 197: 4, 8, 9, 10.  
Th 
10/1 
Fall Holiday      
F 
10/2 
Fall Holiday      
M 
10/5 
3.9 
Practice quiz and discussion  209: 61, 63, 65, 67, 69  
T 
10/6 
3.11 
Quiz on derivatives. Related rates.  Ladder example discussed in detail.  205: 9, 14, 17. CHALLENGE: any one of 44, 45, 46. 
W 
10/7 
Ch. 3 
Review.  
Th 
10/8 
Review  
F 
10/9 
 
TEST on Chapter 3.  
M 
10/12 
4.1 
Approximation  Using e^x to approxiamte 1+x in the Birthday Problem and SS# problem. (Aside on history of logic (Russell, Wittgenstein, Goedel, Turing, von Neuman)  
T 
10/13 
4.1, 4.2 
Approximation (cont.); Least Upper Bounds  Review of SS# problem. Discussion of LUB.  A. Suppose f(N, k) = e^(((k1)(k) / (2N)), N = 1,000,000,000. Find the largest k such that f(N, k) < 1/2. B. Suppose X is a nonempty set of real numbers that has an upper bound. Let U be the set of upper bounds of X. Must U have a least element? (The answer is discussed here.) 
W 
10/14 
4.2 
Maximum Value Theorem, Maxima on closed intervals  Optional notes showing how to derive the MVT from the least upper bound principle here. (These note will almost certainly be incomprehensibe to you. If they interest you and you want to understand them, I'll explain them to you in my office.)  Hand these in Friday, 10/16 > 228: 25, 29, 33, 37, 41, 45 
Th 
10/15 
4.2 
Rolle's Theorem  The lecture concentrated on the idea that mathematics is both a system of notation and techniques for representing and solving problems AND a structured, logical domain of knowledge. I drew a chart on the board showing how many of the concepts we have been discussing come together in Rolle's Theorem.  230: 87, 88 
F 
10/16 
4.3 
Mean Value Theorem  Careful proof of MVT, based on Rolle.  
M 
10/19 
4.3 
Increasing and decreasing functions  
T 
10/20 
4.3 
237: 27, 29, 31, 39, 49  
W 
10/21 
4.4 
Concavity  244: 37, 41, 44, 50  
Th 
10/22 
4.5 
End behavior of polynomials  Large numbers (names)  Suppose f(x) = a_n x^n + ...+ a_0 is a polynomial of degree n with positive leading coefficient. Let M > 0. Find x_0 so that x > x_0 implies f(x) > M. 
F 
10/23 
4.5 
Rational functions and asymptotes  258: 79, 81, 83, 87, 91. Complete work on problem from yesterday.  
M

10/26 
4.6 
Applied Optimization  Agenda for the week: we'll have optimization problems in homework every day this week, and will review previous night's work at the beginning of each class; other new topics will be introduced as noted.  2667: 11, 24, 25. Work sheet. 
T

10/27 
4.6 
More optimization  Examined HW.  Suppose C = a x + b y and A = x y, where a and b are positive constants. Maximize A if C is fixed. Minimize C if A is fixed. 
W

10/28 
4.7 
l'Hopital's rule  267: 36, 50. 277: 1, 5, 9, 13, 15, 19, 21.  
Th

10/29 
4.8 
Newton's Method  266: 16. 278: 41, 43, 45, 47, 49. 283: 5. Investigate f(x) = x^(x^(x^...))) and its inverse function g(x) = x^(1/x).  
F

10/30 
4.9 
Antiderivatives  
M

11/2 

T

11/3 

W

11/4 
Chapter 4 test  
Th

11/5 

F

11/6 

M 
11/9 

T 
11/10 